NAEP Analysis and Scaling → Estimation of Population and Student Group Distributions → Examining the Population-Structure Models Used in NAEP → Proportion of Variance Accounted For by Principal Components Used in NAEP Population-Structure Models → Proportion of Variance of the Group-Defining Contrasts Accounted for by the Principal Components Used in the Population-Structure Model, Grade 4 Reading Combined National and State Assessments: 2011

NAEP Technical DocumentationProportion of variance of the group-defining contrasts accounted for by the principal components used in the population-structure model, grade 4 reading combined national and state assessments: 2011

Type of contrast	Number of contrasts	Mean	Minimum	Maximum	Number of contrasts by proportion1 of variance explained
					0.00 - 0.70	0.70 - 0.80	0.80 - 0.90	0.90 - 0.95	0.95 - 1.00
1 (Total Variance – Residual Variance)/Total Variance, where Total Variance consists of both sampling and measurement error variance. NOTE: NIES = National Indian Education Study; SD/ELL = Students with disabilities/English language learners. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2011 Reading Assessment.
All contrasts	1816	0.90	0.63	1.00	12	90	716	604	394
Student questionnaire	48	0.90	0.72	0.99	0	8	9	11	20
Major reporting variables	212	0.92	0.67	1.00	2	3	54	85	68
Interactions between reporting variables	275	0.89	0.63	0.98	7	15	99	110	44
Teacher questionnaire	521	0.91	0.71	0.99	0	23	179	164	155
School questionnaire	421	0.90	0.75	0.99	0	8	203	158	52
NIES questionnaire	297	0.87	0.68	0.99	3	31	159	68	36
SD/ELL questionnaire	42	0.92	0.77	1.00	0	2	13	8	19

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